1. For each of the following, indicate whether it is a question that involves permutations, combinations, or neither, and then a
1 answer:
Answer:
Step-by-step explanation:
we are given some scenerios and we are to find out the total number of ways after mentioning permutations, combinations, or neither
a. How many ways can a coach choose two co-captains from 16 players in the basketball team?
Combination because both are having same position so order does not matter
16C2 = 120
b. In how many ways can seven questions out of ten be chosen on an examination?
Combinations because order of question does not matter.
10C7 = 10C3 = 120
c. Find the number of ways that 10 women in the finals of the skateboard street competition can finish first, second, and third in the X Games final.
Here order matters. Hence permutation
10P3 = 720
d. A postal zip code contains five digits. How many different zip codes can be made with the digits 0–9? Assume a digit can be repeated.
Here repitition is allowed. So neither permutation nor combination.
No of ways =
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Answer:
<h2>A, C</h2>Step-by-step explanation:
The distributive property:
<em>a(b + c) = ab + ac </em>or<em> a(b - c) = ab - ac</em>
<em></em>
Locate the highest or lowest point on the graph. In this case, there is no highest point. There is only the lowest point. That lowest point is (2,0).
The y coordinate of that lowest point is y = 0. This is the smallest y can be. The value of y cannot be any smaller. This forms the left boundary of the interval notation answer.
There is no upper boundary on how high y can go. It can grow forever. Therefore the right boundary of the interval is infinity
This is why the answer is the interval notation answer
The square bracket indicates "include this value in the set" while a parenthesis says "exclude this value". We can never reach infinity so infinity is always with a parenthesis
Final Answer: Choice A
Note: the interval notation answer for choice A is the same as writing
(y is greater than or equal to 0)
The y coordinate of that lowest point is y = 0. This is the smallest y can be. The value of y cannot be any smaller. This forms the left boundary of the interval notation answer.
There is no upper boundary on how high y can go. It can grow forever. Therefore the right boundary of the interval is infinity
This is why the answer is the interval notation answer
The square bracket indicates "include this value in the set" while a parenthesis says "exclude this value". We can never reach infinity so infinity is always with a parenthesis
Final Answer: Choice A
Note: the interval notation answer for choice A is the same as writing
Answer:
If you mean only one rational solution, the answer is
If you mean at least 1 rational solution, the answer is
Step-by-step explanation:
Let's calculate the discriminant.
Now, remember that:
Therefore, I will just consider the first two cases.
and
Answer:
We conclude that
- The angle ∠1 = x = 36°
- The angle ∠2 = 4x = 4(36°) = 144°
Step-by-step explanation:
Given
<1 and <2 form a linear pair
m∠1 = 4m∠2
To determine
Find the measure of each of the two angles.
<u>Important Points about linear pair:</u>
- We know that when two lines meet or intersect, we get a linear pair of angles.
- Linear pairs are basically two adjacent angles that form a line.
- The measure of two adjacent angles forming a straight line is 180, meaning they are supplementary.
As
<1 and <2 form a linear pair
m∠1 = 4m∠2
In other words, angle 1 is 4 times the measure of angle ∠2.
Let the angle ∠1 be = x
As the angle 1 is 4 times the measure of angle ∠2, so
The angle 2 will be = 4x
As <1 and <2 forms a linear pair, thus the measure of the sum of <1 and <2 will be 180°, so
divide both sides by 5
Thus, we conclude that
- The angle ∠1 = x = 36°
- The angle ∠2 = 4x = 4(36°) = 144°